I'm trying to make sure I understand this. Atc says he was instructed to exit on a "forward". Does he mean a high speed exit? Is he yelling at him because he did something else like turn back onto a reverse high speed or skip one the controller thought he could make?

We don't really have enough context to know exactly. If you look at the airport diagram there is a turnoff at the end of 19L and a couple of high speed turnoffs. I speculate from "exit straight ahead, c'mon get off the runway right away" that they were past the last high speed turnoff. Sounds like N8860 was taking its sweet time picking somewhere to turn, or maybe came to a stop or taxiing very slowly. Rule one is minimum time on the runway. The controller cannot allow the trailing aircraft to land until the preceding aircraft is across the hold short line on its turnoff and would have had to issue a go-around.

I don't know when this happened but I think we would have to check an archive file to see what instructions the aircraft was given in the landing clearance and up to the time when he started chastising them.

Not exactly. Once you are cleared to land you own the runway up until the time you have landed, rolled out, and slowed sufficiently to make a turnoff and completely crossed the hold short line of that turnoff. The controller cannot give you any further instructions until then (unless to go around due to some condition that has come up.) There is no way to predict how the rollout will complete ahead of time. The one exception to this is a land and hold short where you make a contract in advance not to go past a particular spot on the landing runway and you do not accept the landing clearance if you choose not to make that contract. Typically once you are sufficiently slowed to make it clear what is possible, the controller may say "left at Bravo ground point eight when off the runway."

As I mentioned after you have successfully rolled out and slowed sufficiently to safely turn the aircraft, rule one is minimum time on the runway. We have a following aircraft and the controller has sequenced things to anticipate how long N8860 will probably need to do all the above. If N8860 takes longer, the controller may have to have the following aircraft go around because of the runway being occupied. In this case the controller felt strongly that N8860 was not clearing the runway in an expeditious fashion to the point where it should be sanctioned.

I think in order to know why the controller was so upset you would have had to be there watching.

I listened to the 1R/19L tower feed. N8860 was asked to expedite off the runway (19L) at K7. a full 40 seconds later he was asked to expedite off the runway at the end, and told that there was an aircraft on short final. He then switched to ground, and still wasn't completely clear. So he was really taking his time, impossible to know why.

Doesn't matter why Marty is correct we own the runway for as long as necessary. The controller can never "write us up" for flying the airplane as we see fit. Sounds like this controller was on a bit of a power trip.